Question: $a_n={\dfrac{(-2)^{n-1}}{\sqrt{n+1}}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Explanation: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=2$ Since the limit, $2$, is greater than $1$, the ratio rest tells us that the series diverges.